Origin of intrinsic Gilbert damping

Abstract

The damping of magnetization, represented by the rate at which it relaxes to equilibrium, is successfully modeled as a phenomenological extension in the Landau-Lifschitz-Gilbert equation. This is the damping torque term known as Gilbert damping and its direction is given by the vector product of the magnetization and its time derivative. Here we derive the Gilbert term from first principles by a non-relativistic expansion of the Dirac equation. We find that the Gilbert term arises when one calculates the time evolution of the spin observable in the presence of the full spin-orbital coupling terms, while recognizing the relationship between the curl of the electric field and the time varying magnetic induction.

5 pages, 1 figures

References in corpus (7)

• Roles of non-equilibrium conduction electrons on magnetization dynamics of ferromagnets
• Nonlocal magnetization dynamics in ferromagnetic heterostructures
• Out-of-plane spin polarization from in-plane electric and magnetic fields
• Mean-field magnetization relaxation in conducting ferromagnets
• Spin dynamics from time-dependent spin density-functional theory
• Inhomogeneous Gilbert damping from impurities and electron-electron interactions
• Gilbert damping and spin Coulomb drag in a magnetized electron liquid with spin-orbit interaction

Cited by in corpus (40)

• Quantum magnonics: when magnon spintronics meets quantum information science
• Electrical Detection of Magnetization Dynamics via Spin Rectification Effects
• Experimental Investigation of Temperature-Dependent Gilbert Damping in Permalloy Thin Films
• Low magnetic damping of ferrimagnetic GdFeCo alloys
• Relativistic theory of magnetic inertia in ultrafast spin dynamics
• Perspective: non-Hermitian physics in magnetic systems
• Relaxation Mechanism for Ordered Magnetic Materials
• Role of Element-Specific Damping on the Ultrafast, Helicity-Independent All-Optical Switching Dynamics in Amorphous (Gd,Tb)Co Thin Films
• $\Lambda$ and $\bar{\Lambda }$ spin interaction with meson fields generated by the baryon current in high energy nuclear collisions
• Predicting New Iron Garnet Thin Films with Perpendicular Magnetic Anisotropy
• Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms
• Respective influence of in-plane and out-of-plane spin-transfer torques in magnetization switching of perpendicular magnetic tunnel junctions
• Non-Hermitian skin effect in magnetic systems
• Spin Pumping in Ion-beam Sputtered Co_{2}FeAl/Mo Bilayers:Interfacial Gilbert Damping
• Phenomenological description of the nonlocal magnetization relaxation in magnonics, spintronics, and domain-wall dynamics
• Influence of heavy metal materials on magnetic properties of Pt/Co/heavy metal tri-layered structures
• Study of spin pumping in Co thin film vis-a-vis seed and capping layer using ferromagnetic resonance spectroscopy
• Strong magnon softening in tetragonal FeCo compounds
• Unified theory of magnetization dynamics with relativistic and nonrelativistic spin torques
• Magnon decay theory of Gilbert damping in metallic antiferromagnets
• Influence of inter-sublattice coupling on the terahertz nutation spin dynamics in antiferromagnets
• Comparative study of methodologies to compute the intrinsic Gilbert damping: interrelations, validity and physical consequences
• Solitons in a continuous classical Haldane-Shastry spin chain
• Theory of magnetic inertial dynamics in two-sublattice ferromagnets
• Signatures of relativistic spin-light coupling in ultrafast magneto-optical pump-probe experiments
• Influence of non-local damping on magnon properties of ferromagnets
• Correlation Effects in the Stochastic Landau-Lifshitz-Gilbert Equation
• Another view on Gilbert damping in two-dimensional ferromagnets
• Reversal time of the magnetization of magnetic nanoparticles at very low damping
• Dynamics of the relativistic electron spin in an electromagnetic field
• Interplay of Wave Localization and Turbulence in Spin Seebeck Effect
• Spin Transfer from the point of view of the ferromagnetic degrees of freedom
• Universal spin wave damping in magnetic Weyl semimetals
• A microscopic model for current-induced switching of magnetization for half-metallic leads
• Damping dependence of spin-torque effects in thermally assisted magnetization reversal
• Microwave induced tunable subharmonic steps in superconductor-ferromagnet-superconductor Josephson junction
• Conservative effects in spin-transfer-driven magnetization dynamics
• High-frequency behavior of FeN thin films fabricated by reactive sputtering
• Emerging magnetic nutation
• Spin relaxation signature of colossal magnetic anisotropy in platinum atomic chains